Modeling financial data using the multivariate generalized hyperbolic distribution and copula.
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Date
2015
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Abstract
Financial data usually possess some characteristics, such as volatility clustering, asymmetry,
heavy and semi-heavy tails thus, making it difficult, if not impossible, to use
Normal distribution to model them. Statistical analyzis shows that the Generalized
hyperbolic distribution is appropriate for capturing these characteristics. This research
shows that the USD/ZAR, All shares, Gold mining as well as the the S&P
500 returns are best modeled with the Skew t, generalized hyperbolic, hyperbolic,
generalized hyperbolic distributions respectively based on AIC and Value-at-Risk
(VAR) backtesting. Further multivariate analyzis of these returns based on the kernel
smoothing goodness of fit shows that; the multivariate affine normal inverse gaussian
(MANIG) distribution provides the best fit for the affine models. Likewise, the multivariate
normal inverse gaussian (MNIG) distribution based on AIC provides the best
model for the four returns. Finally, the positive tail dependencies exhibited between
the All shares and Gold mining returns as well as All shares and S&P 500 returns is
best modeled with the Gumbel and Clayton copulas respectively. While the negative
dependencies between the USD/ZAR returns and other returns is modeled with the
Frank copula.
Description
Master of Science in Statistics. University of KwaZulu-Natal, Durban 2015.
Keywords
Theses - Statistics.